(1) The paradigmatic type of synthetic a priori knowledge that was Euclidean geometry, when asserted as a universally true theory of space, has been shown to be severely contradicted by empirical evidence – and this is not what we would expect to find if this theory really was necessarily true and an irrefutable theory of reality.Ultimately, we can reject synthetic a priori knowledge by inference to the best explanation and Ockham’s razor.
(2) We can eliminate the problem of proposed synthetic a priori knowledge by carefully separating pure maths/pure geometry (which is analytic a priori and necessarily true, but not describing reality) from applied maths/applied geometry (which is asserted as true of reality but is synthetic a posteriori and contingent).
For example, most of mathematics can be clearly explained as an analytic a priori system, as derived from pure logic and set theory (Schwartz 2012: 19), as shown by the work of Frege, Russell, and Whitehead.
(3) From (1) and (2), we can satisfactorily explain proposed synthetic a priori knowledge either as (i) analytic a priori or (ii) synthetic a posteriori, eliminating a complex and unnecessary category.
Schwartz, Stephen P. 2012. A Brief History of Analytic Philosophy: From Russell to Rawls. Wiley-Blackwell, Chichester, UK.
What about NECESSARY a posteriori truths? for example, descriptive marginalism as a theory of value rests on the divisibility of goods, the divisibility of time, the notion of scarcity, the the fact the we unconsciously rank ordinal preferences. It DOES NOT mean that those preferences are fixed and unchanging, nor does it mean that they are in any sense "rational" (cigarette smokers might have a revealed utility function 10 cigarettes per day after which their pleasure rapidly diminishes, this doesn't have ANYTHING to do with homo economicus) nor does it mean the the law of diminishing returns is absolutely valid, (given two or three sets of variable inputs, constant or increasing returns might be possible, nor does it mean that businesses set up two way auction markets to determine prices when clearly there are large (But that doesn't mean anything, because clearly in the long run consumers rule by "hitting the ask" every time they buy and in very small businesses with thin markets, EVEN ONE consumer may mean the difference between profit and loss- Which is why I roll my eyes whenever I read yet another one of your ENDLESS posts on mark-up pricing, which doesn't mean much in the long runReplyDelete
I saw a commentator "Nathan" point you to a neoclassical take on the Cambridge Capital Controversies.
Here's my take. First, what in GOD's name is the rate of Profit? :-) I read the Wikipedia page, and instead of clarifying matters, it confused me more. What is it in specific terms that an investor can understand? Is it Gross Profit Margin, Net Profit Margin, Average Profit Margin by Sector, Return on Assets, return on Equity, what?
Second, the existence of money and aggregated demand simplifies things immensely. We can say that aggregate demand determines employment and the godawful Marxian term rate of profit across the whole economy, when we add the money value of discrete pieces of capital. If we do this. we realize that it is the government's(treasury or central bank) job to maintain an adequate level of aggregate demand and NGDP growth
Second, we can analyze the rate of return in one class of capital (as opposed to all capital) as the marginal productivity of capital minus its marginal cost. The rate of "interest" is not equal to the marginal productivity of capital, the MPC EXCEEDS the rate of interest. ( The two are related but not the same you have to account for the cost of the machine, depreciation, and positive externalities that flow down the generations with an invention after its patents expire)
Your comment is all over the place.Delete
Regarding necessary a posteriori truths, they are supposed to be ontologically necessarily.
So if, say, some neoclassical really thinks the law of diminishing marginal utility is ontologically necessarily, that is straightforwardly false -- as clear exceptions exist.
First, what in GOD's name is the rate of Profit?Delete
Ed: Think ROI. So, Net Profit/Costs, a.k.a. (Revenues - Costs)/Costs. Insofar as we're discussing Marxists (per your comment), the relevant profit measure is analogous to what Godley & Lavoie call "Total Business Profits," or EBITDA.
Matias Vernengo has a follow-up piece on his critique of Bob Murphy.
Thanks for the link!Delete